parallelizable

Input interpretation

parallelizable

Definition

A hypersphere S^n is parallelizable if there are n vector fields that are linearly independent at each point. There exist only three parallelizable spheres: S^1, S^3, and S^7 (Adams 1958, 1960, Le Lionnais 1983). More generally, an n-dimensional manifold M is parallelizable if its tangent bundle T M is a trivial bundle (i.e., if T M is globally of the form M×R^n).
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Related terms

manifold | sphere | tangent bundle | trivial bundle | vector bundle

Subject classifications

MathWorld

topological structures | n-dimensional geometry
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